Standard units and conversions

OCR J560 expects fluent conversion between metric units. Foundation papers test simple conversions; Higher tier mixes them into multi-step problems where a single error cascades.

Length

| 1 km | = 1000 m | | 1 m | = 100 cm | | 1 cm | = 10 mm | | 1 m | = 1000 mm |

Mass

| 1 tonne | = 1000 kg | | 1 kg | = 1000 g | | 1 g | = 1000 mg |

Capacity / volume

| 1 litre | = 1000 ml | | 1 ml | = 1 cm³ | | 1 litre | = 1000 cm³ | | 1 m³ | = 1000 litres |

Time

| 1 minute | = 60 s | | 1 hour | = 60 min = 3600 s | | 1 day | = 24 hours |

Decimal hours: 30 min = 0.5 h; 15 min = 0.25 h; 45 min = 0.75 h.

Money

UK: £1 = 100p. Always express money to 2 decimal places (e.g. £4.50, not £4.5).

Area conversions (a Higher tier trap)

Length factors square when converting area:

• 1 m² = (100 cm)² = 10,000 cm².
• 1 cm² = (10 mm)² = 100 mm².
• 1 km² = 1,000,000 m².

Volume conversions

Length factors cube:

• 1 m³ = (100 cm)³ = 1,000,000 cm³.
• 1 cm³ = 1000 mm³.

Compound units (rates)

Speed: m/s, km/h, mph. To convert m/s to km/h, multiply by 3.6 (since 1 m/s = 3600/1000 = 3.6 km/h).

Density: g/cm³ or kg/m³. 1 g/cm³ = 1000 kg/m³.

OCR mark scheme conventions

• M1 for the conversion factor used.
• A1 for the converted value with units.
• "State your units" means write them explicitly — answer alone is incomplete.